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<div class="title">arch/AVX512/MathFunctions.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2016 Pedro Gonnet (pedro.gonnet@gmail.com)</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;../../InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#if EIGEN_HAS_AVX512_MATH</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#define EIGEN_DECLARE_CONST_Packet16f(NAME, X) \</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">  const Packet16f p16f_##NAME = pset1&lt;Packet16f&gt;(X)</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160; </div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#define EIGEN_DECLARE_CONST_Packet16f_FROM_INT(NAME, X) \</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">  const Packet16f p16f_##NAME =  preinterpret&lt;Packet16f,Packet16i&gt;(pset1&lt;Packet16i&gt;(X))</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="preprocessor">#define EIGEN_DECLARE_CONST_Packet8d(NAME, X) \</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">  const Packet8d p8d_##NAME = pset1&lt;Packet8d&gt;(X)</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">#define EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(NAME, X) \</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="preprocessor">  const Packet8d p8d_##NAME = _mm512_castsi512_pd(_mm512_set1_epi64(X))</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#define EIGEN_DECLARE_CONST_Packet16bf(NAME, X) \</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">  const Packet16bf p16bf_##NAME = pset1&lt;Packet16bf&gt;(X)</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="preprocessor">#define EIGEN_DECLARE_CONST_Packet16bf_FROM_INT(NAME, X) \</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="preprocessor">  const Packet16bf p16bf_##NAME =  preinterpret&lt;Packet16bf,Packet16i&gt;(pset1&lt;Packet16i&gt;(X))</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;plog&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  <span class="keywordflow">return</span> plog_float(_x);</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;}</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160; </div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;plog&lt;Packet8d&gt;(<span class="keyword">const</span> Packet8d&amp; _x) {</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  <span class="keywordflow">return</span> plog_double(_x);</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;}</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160; </div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, plog)</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog)</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;plog2&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  <span class="keywordflow">return</span> plog2_float(_x);</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;}</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;plog2&lt;Packet8d&gt;(<span class="keyword">const</span> Packet8d&amp; _x) {</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="keywordflow">return</span> plog2_double(_x);</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;}</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, plog2)</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog2)</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">// Exponential function. Works by writing &quot;x = m*log(2) + r&quot; where</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">// &quot;m = floor(x/log(2)+1/2)&quot; and &quot;r&quot; is the remainder. The result is then</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">// &quot;exp(x) = 2^m*exp(r)&quot; where exp(r) is in the range [-1,1).</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;pexp&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(1, 1.0f);</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(half, 0.5f);</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(127, 127.0f);</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160; </div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(exp_hi, 88.3762626647950f);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(exp_lo, -88.3762626647949f);</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(cephes_LOG2EF, 1.44269504088896341f);</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p0, 1.9875691500E-4f);</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p1, 1.3981999507E-3f);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p2, 8.3334519073E-3f);</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p3, 4.1665795894E-2f);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p4, 1.6666665459E-1f);</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p5, 5.0000001201E-1f);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="comment">// Clamp x.</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  Packet16f x = pmax(pmin(_x, p16f_exp_hi), p16f_exp_lo);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <span class="comment">// Express exp(x) as exp(m*ln(2) + r), start by extracting</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <span class="comment">// m = floor(x/ln(2) + 0.5).</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  Packet16f m = _mm512_floor_ps(pmadd(x, p16f_cephes_LOG2EF, p16f_half));</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="comment">// Get r = x - m*ln(2). Note that we can do this without losing more than one</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <span class="comment">// ulp precision due to the FMA instruction.</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  EIGEN_DECLARE_CONST_Packet16f(nln2, -0.6931471805599453f);</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  Packet16f r = _mm512_fmadd_ps(m, p16f_nln2, x);</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  Packet16f r2 = pmul(r, r);</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  Packet16f r3 = pmul(r2, r);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  <span class="comment">// Evaluate the polynomial approximant,improved by instruction-level parallelism.</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  Packet16f y, y1, y2;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  y  = pmadd(p16f_cephes_exp_p0, r, p16f_cephes_exp_p1);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  y1 = pmadd(p16f_cephes_exp_p3, r, p16f_cephes_exp_p4);</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  y2 = padd(r, p16f_1);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  y  = pmadd(y, r, p16f_cephes_exp_p2);</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  y1 = pmadd(y1, r, p16f_cephes_exp_p5);</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  y  = pmadd(y, r3, y1);</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  y  = pmadd(y, r2, y2);</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  <span class="comment">// Build emm0 = 2^m.</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  Packet16i emm0 = _mm512_cvttps_epi32(padd(m, p16f_127));</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  emm0 = _mm512_slli_epi32(emm0, 23);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160; </div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  <span class="comment">// Return 2^m * exp(r).</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <span class="keywordflow">return</span> pmax(pmul(y, _mm512_castsi512_ps(emm0)), _x);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;}</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;pexp&lt;Packet8d&gt;(<span class="keyword">const</span> Packet8d&amp; _x) {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="keywordflow">return</span> pexp_double(_x);</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;}</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, pexp)</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexp)</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;EIGEN_STRONG_INLINE Packet16h pfrexp(<span class="keyword">const</span> Packet16h&amp; a, Packet16h&amp; exponent) {</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  Packet16f fexponent;</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  <span class="keyword">const</span> Packet16h out = float2half(pfrexp&lt;Packet16f&gt;(half2float(a), fexponent));</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  exponent = float2half(fexponent);</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;  <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;}</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;EIGEN_STRONG_INLINE Packet16h pldexp(<span class="keyword">const</span> Packet16h&amp; a, <span class="keyword">const</span> Packet16h&amp; exponent) {</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  <span class="keywordflow">return</span> float2half(pldexp&lt;Packet16f&gt;(half2float(a), half2float(exponent)));</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;}</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;EIGEN_STRONG_INLINE Packet16bf pfrexp(<span class="keyword">const</span> Packet16bf&amp; a, Packet16bf&amp; exponent) {</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  Packet16f fexponent;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  <span class="keyword">const</span> Packet16bf out = F32ToBf16(pfrexp&lt;Packet16f&gt;(Bf16ToF32(a), fexponent));</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  exponent = F32ToBf16(fexponent);</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;}</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;EIGEN_STRONG_INLINE Packet16bf pldexp(<span class="keyword">const</span> Packet16bf&amp; a, <span class="keyword">const</span> Packet16bf&amp; exponent) {</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;  <span class="keywordflow">return</span> F32ToBf16(pldexp&lt;Packet16f&gt;(Bf16ToF32(a), Bf16ToF32(exponent)));</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;}</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="preprocessor">#if EIGEN_FAST_MATH</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;psqrt&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  <span class="keywordflow">return</span> generic_sqrt_newton_step&lt;Packet16f&gt;::run(_x, _mm512_rsqrt14_ps(_x));</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;}</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;psqrt&lt;Packet8d&gt;(<span class="keyword">const</span> Packet8d&amp; _x) {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="comment">// Double requires 2 Newton-Raphson steps for convergence.</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keywordflow">return</span> generic_sqrt_newton_step&lt;Packet8d, <span class="comment">/*Steps=*/</span>2&gt;::run(_x, _mm512_rsqrt14_pd(_x));</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;}</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;EIGEN_STRONG_INLINE Packet16f psqrt&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; x) {</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  <span class="keywordflow">return</span> _mm512_sqrt_ps(x);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;}</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160; </div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;EIGEN_STRONG_INLINE Packet8d psqrt&lt;Packet8d&gt;(<span class="keyword">const</span> Packet8d&amp; x) {</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  <span class="keywordflow">return</span> _mm512_sqrt_pd(x);</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;}</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160; </div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, psqrt)</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psqrt)</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="comment">// prsqrt for float.</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="preprocessor">#if defined(EIGEN_VECTORIZE_AVX512ER)</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160; </div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;EIGEN_STRONG_INLINE Packet16f prsqrt&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; x) {</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  <span class="keywordflow">return</span> _mm512_rsqrt28_ps(x);</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;}</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="preprocessor">#elif EIGEN_FAST_MATH</span></div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;prsqrt&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="keywordflow">return</span> generic_rsqrt_newton_step&lt;Packet16f, <span class="comment">/*Steps=*/</span>1&gt;::run(_x, _mm512_rsqrt14_ps(_x));</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;}</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160; </div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, prsqrt)</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, prsqrt)</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160; </div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="comment">// prsqrt for double.</span></div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;<span class="preprocessor">#if EIGEN_FAST_MATH</span></div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;prsqrt&lt;Packet8d&gt;(<span class="keyword">const</span> Packet8d&amp; _x) {</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="preprocessor">  #ifdef EIGEN_VECTORIZE_AVX512ER</span></div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    <span class="keywordflow">return</span> generic_rsqrt_newton_step&lt;Packet8d, <span class="comment">/*Steps=*/</span>1&gt;::run(_x, _mm512_rsqrt28_pd(_x));</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="preprocessor">  #else</span></div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    <span class="keywordflow">return</span> generic_rsqrt_newton_step&lt;Packet8d, <span class="comment">/*Steps=*/</span>2&gt;::run(_x, _mm512_rsqrt14_pd(_x));</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="preprocessor">  #endif</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;}</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160; </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_STRONG_INLINE Packet16f preciprocal&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; a) {</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="preprocessor">#ifdef EIGEN_VECTORIZE_AVX512ER</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  <span class="keywordflow">return</span> _mm512_rcp28_ps(a);</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keywordflow">return</span> generic_reciprocal_newton_step&lt;Packet16f, <span class="comment">/*Steps=*/</span>1&gt;::run(a, _mm512_rcp14_ps(a));</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;}</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, preciprocal)</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, preciprocal)</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;Packet16f plog1p&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;  <span class="keywordflow">return</span> generic_plog1p(_x);</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;}</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160; </div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, plog1p)</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog1p)</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;Packet16f pexpm1&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keywordflow">return</span> generic_expm1(_x);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;}</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160; </div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, pexpm1)</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexpm1)</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_HAS_AVX512_MATH</span></div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160; </div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160; </div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;psin&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  <span class="keywordflow">return</span> psin_float(_x);</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;}</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160; </div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;pcos&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  <span class="keywordflow">return</span> pcos_float(_x);</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;}</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;ptanh&lt;Packet16f&gt;(<span class="keyword">const</span> Packet16f&amp; _x) {</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  <span class="keywordflow">return</span> internal::generic_fast_tanh_float(_x);</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;}</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, psin)</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, pcos)</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;F16_PACKET_FUNCTION(Packet16f, Packet16h, ptanh)</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160; </div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psin)</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pcos)</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;BF16_PACKET_FUNCTION(Packet16f, Packet16bf, ptanh)</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160; </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;}  <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160; </div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
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